Question

Express the following in the form a+ib, where a,b€R. State the value of a,b i(4+3i)/(1-i)

Answer 1

we have to find values of a and b if

a + ib = i(4 + 3i)/(1 - i)

⇒a + ib = (i × 4 + i × 3i)/(1 - i)

⇒a + ib = (4i + 3i²)/(1 - i)

⇒a + ib = {4i + 3(-1)}/(1 - i) [we know, i² = -1]

⇒a + ib = {4i - 3}/(1 - i)

⇒ a + ib = (4i - 3)/(1 - i) × (1 + i)/(1 + i)

⇒a + ib = (4i - 3)(1 + i)/(1 - i)(1 + i)

⇒a + ib = {4i(1 + i) - 3(1 + i)}/(1² - i²)

⇒a + ib = {4i + 4i² - 3 - 3i}/(1 + 1)

⇒ a + ib = (i - 4 - 3)(2)

⇒a + ib = (-7/2) + (1/2)i

hence, a = -7/2 and b = 1/2